Kotlyarova, Yulia, Schafgans, Marcia M. A. and Zinde‐Walsh, Victoria (2011) Adapting kernel estimation to uncertain smoothness. Econometrics Papers, EM/2011/557. Suntory and Toyota International Centres for Economics and Related Disciplines, London School of Economics and Political Science, London, UK.
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For local and average kernel based estimators, smoothness conditions ensure that the kernel order determines the rate at which the bias of the estimator goes to zero and thus allows the econometrician to control the rate of convergence. In practice, even with smoothness the estimation errors may be substantial and sensitive to the choice of the bandwidth and kernel. For distributions that do not have sufficient smoothness asymptotic theory may importantly differ from standard; for example, there may be no bandwidth for which average estimators attain root-n consistency. We demonstrate that non-convex combinations of estimators computed for different kernel/bandwidth pairs can reduce the trace of asymptotic mean square error relative even to the optimal kernel/bandwidth pair. Our combined estimator builds on these results. To construct it we provide new general estimators for degree of smoothness, optimal rate and for the biases and covariances of estimators. We show that a bootstrap estimator is consistent for the variance of local estimators but exhibits a large bias for the average estimators; a suitable adjustment is provided.
|Item Type:||Monograph (Discussion Paper)|
|Additional Information:||© 2011 The Authors|
|Uncontrolled Keywords:||nonparametric estimation, kernel based estimator, combined stimator, variance bootstrap|
|Library of Congress subject classification:||H Social Sciences > HB Economic Theory|
|Journal of Economic Literature Classification System:||C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General > C14 - Semiparametric and Nonparametric Methods|
|Sets:||Departments > Economics
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